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1) Heat the oil in a heavy 24-cm-diameter frying-pan over medium heat. Add the potato, onion, and garlic. Season the potato mixture with salt and pepper, to taste. Saute over medium-low heat until the potato is golden and crisp on the outside, tender inside, about 7 to 10 minutes.

2) Preheat the overhead grill. Whisk the eggs, cream, Parmesan, prosciutto, and basil in a medium bowl to blend. Stir the egg mixture into the potato mixture in the skillet. Cook over medium-low heat until the egg mixture is almost set but the top is still loose, about 3 minutes.

3) Place the frying-pan under the grill. Grill until the top is set and golden brown, about 4 minutes. Using a rubber spatula, loosen the frittata from pan and slide the frittata onto a cutting board. Cut the frittata into 12 wedges.

4) Split open each bread piece. Toast the bread on a grill pan until golden. You can also grill the bread cut side up until golden, about 1 to 2 minutes, keeping a careful watch on the bread since they can easily burn. Butter the cut sides of the toasted bread. Arrange a frittata wedge on each bottom piece of bread. Cover with the bread tops and serve.